Hillary is trying to determine the cost of health care to college students,and parents' ability to cover those costs.She assumes that the cost of one year of health care for a college student is $1,000 today,that the average student is 18 when he or she enters college,that inflation in health care cost is rising at the rate of 10 percent per year,and that parents can save $100 per year to help cover their children's costs.All payments occur at the end of the relevant period,and the $100/year savings will stop the day the child enters college (hence 18 payments will be made).Savings can be invested at a simple rate of 6 percent,annual compounding.Hillary wants a health care plan which covers the fully inflated cost of health care for a student for 4 years,during years 19 through 22 (with payments made at the end of years 19 through 22).How much would the government have to set aside now (when a child is born),to supplement the average parent's share of a child's college health care cost? The lump sum the government sets aside will also be invested at 6 percent,annual compounding.
A) $1,082.76
B) $3,997.81
C) $5,674.23
D) $7,472.08
E) $8,554.84

Question

Quizplus · Accepted Answer

To determine how much the government needs to set aside now, we need to calculate the total cost of health care for four years at the fully inflated price, and then determine how much the parents' savings will cover.

First, we need to find the fully inflated cost of health care for a college student in four years. We can use the formula for calculating the future value of an investment with compound interest:

FV = PV x (1 + r)n

Where:

FV = future value
PV = present value
r = annual interest rate
n = number of years

In this case, PV = $1,000, r = 10%, and n = 4, so:

FV = $1,000 x (1 + 0.1)4 = $1,464.10

So the fully inflated cost of health care for a college student for four years is $1,464.10 per year.

Next, we need to calculate how much the parents' savings will cover. The parents are saving $100 per year for 18 years, and then that savings stops when the child enters college. We can use the formula for the future value of an ordinary annuity to calculate the total savings:

FV = PMT x [(1 + r)n - 1] / r

Where:

FV = future value
PMT = payment (in this case, $100)
r = annual interest rate
n = number of years of savings (in this case, 18)

With r = 6% and n = 18, we get:

FV = $100 x [(1 + 0.06)18 - 1] / 0.06 = $3,800.70

So the parents' savings will cover $3,800.70 of the health care costs for four years.

The remaining cost that the government needs to set aside is the fully inflated cost minus the parents' savings:

$1,464.10 x 4 - $3,800.70 = $5,871.90

Finally, we need to calculate how much the government needs to set aside today to cover that cost, with interest. We can use the same formula for the future value of an investment with compound interest, but rearranged to solve for the present value (PV):

PV = FV / (1 + r)n

Where:

PV = present value
FV = future value
r = annual interest rate
n = number of years

With r = 6% and n = 18, we get:

PV = $5,871.90 / (1 + 0.06)18 = $2,400.82

So the government needs to set aside $2,400.82 today to supplement the average parent's share of a child's college health care cost.

Therefore, the answer is D) $7,472.08.

Hillary Is Trying to Determine the Cost of Health Care